C.C. de Souza

The node capacitated graph partitioning problem: a computational study

In this paper we consider the problem ofk-partitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition, and the objective of minimizing the sum of the costs of the edges between the subsets of the partition. Based on a study of valid inequalities, we present a variety of separation heuristics for cycle, cycle with ears, knapsack tree and path-block cycle inequalities among others. The separation heuristics, plus primal heuristics, have been implemented in a branch-and-cut routine using a formulation including variables for the edges with nonzero costs and node partition variables. Results are presented for three classes of problems: equipartitioning problems arising in finite element methods and partitioning problems associated with electronic circuit layout and compiler design.

LMI numerical solution for output feedback stabilization

The main objective of this paper is to solve the following stabilizing output feedback control problem. Given matrices (A, B/sub 2/, C/sub 2/) with appropriate dimensions, find (if one exists), a static output feedback gain L such that the closed-loop matrix A-B/sub 2/LC/sub 2/ is asymptotically stable. Using linear matrix inequalities, it is shown that the existence of L is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set. Conditions are provided for global convergence of the min/max algorithm which decomposes the determination of the aforementioned matrix by a sequence of convex programs. Some examples borrowed from the literature are solved hi order to illustrate the theoretical results.

Formulations and valid inequalities for the node capacitated graph partitioning problem

We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts. In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem parameters change.

An Exact and Efficient Algorithm for the Orthogonal Art Gallery Problem

In this paper, we propose an exact algorithm to solve the orthogonal art gallery problem in which guards can only be placed on the vertices of the polygon P representing the gallery. Our approach is based on a discretization of P into a finite set of points in its interior. The algorithm repeatedly solves an instance of the set cover problem obtaining a minimum set Z of vertices of P that can view all points in the current discretization. Whenever P is completely visible from Z, the algorithm halts; otherwise, the discretization is refined and another iteration takes place. We establish that the algorithm always converges to an optimal solution by presenting a worst case analysis of the number of iterations that could be effected. Even though these could theoretically reach 0(n4), our computational experiments reveal that, in practice, they are linear in n and, for n les 200, they actually remain less than three in almost all instances. Furthermore, the low number of points in the initial discretization, 0(n2), compared to the possible O(n4) atomic visibility polygons, renders much shorter total execution times. Optimal solutions found for different classes of instances of polygons with up to 200 vertices are also described.In the reversible conversion of color images to gray ones, colors are mapped to textures and from the textures the receiver can recover the colors, i.e. one may print a color image with a black and white printer and, at a later time, recover colors. Such a method was originally devised using the wavelet transform and replacing high-frequency subbands by subsampled chrominance planes. Here, we propose to improve the original method thorugh the use of a largely redundant representation of the chrominance, with multiple embedding into subbands of a general subband transform. Our results point to minimization of the variance of the error caused by noise when the chrominance is replicated into many subbands and not linearly combined. Derived noise bounds guide us on how many subbands to embed the chrominance. Experimental results were carried for multiple noise levels, models, transform sizes, and number of embedding subbands, demonstrating the theoretical analysis and the method’s potential.

Rearrangement of DNA fragments: a branch-and-cut algorithm

Abstract We consider a problem called minimum k-contig problem (MkCP), whose specialization to an alphabet with four symbols can be seen as a problem that arises in the process of arranging DNA fragments to reconstruct a molecule. We present a graph theoretical formulation of MkCP and mention some extensions. We show this problem to be NP -hard for every k⩾1 (for an alphabet that is not of fixed cardinality). A 0/1 integer linear programming formulation of the problem is given and some results of a branch-and-cut algorithm based on this formulation are discussed.

New branch-and-bound algorithms for k-cardinality tree problems

Abstract Given an undirected graph, the k -cardinality tree problem (KCTP) is the problem of finding a subtree with exactly k edges whose sum of weights is minimum. In this paper we present a lower bound for KCTP based on the work by Kataoka et al. [Kataoka, S., N. Araki and T. Yamada, Upper and lower bounding procedures for the minimum rooted k -subtree problem, European Journal of Operational Research, 122 (2000), 561–569]. This new bound is the basis for the development of a branch-and-bound algorithm for the problem. Experiments carried out on instances from KCTLib revealed that the new exact algorithm largely outperforms the previous approach.

Publications of bone marrow transplants in Latin America. A report of the Latin American Group of Bone Marrow Transplantation

Publications of bone marrow transplants in Latin America. A report of the Latin American Group of Bone Marrow Transplantation

Upper and lower bounding procedures for the minimum caterpillar spanning problem

Abstract A spanning caterpillar in a graph is a tree composed by a path such that all vertices not in the path are leaves. In the Minimum Spanning Caterpillar Problem (MSCP) each edge has two costs: a path cost when it belongs to the path and a connection cost when it is incident to a leaf. The goal is to find a spanning caterpillar minimizing the sum of all path and connection costs. In this paper we formulate the as a minimum Steiner arborescence problem. This reduction is the basis for the development of an efficient branch-and-cut algorithm for the MSCP. We als developed a GRASP heuristic to generate primal bounds. Experiments carried out on instances adapted from TSPLIB 2.1 revealed that the exact algorithm is capable to solve to optimality instances with up to 300 vertices in reasonable time. They also showed that our heuristic yields very high quality solutions.

A third generation regimen VACOP-B with or without adjuvant radiotherapy for aggressive localized non-Hodgkin's lymphoma: report from the Italian Non-Hodgkin's Lymphoma Co-operative Study Group

The objective of this multicenter prospective study was to determine the clinical efficacy and toxicity of a polychemotherapeutic third generation regimen, VACOP-B, with or without radiotherapy as front-line therapy in aggressive localized non-Hodgkins lymphoma. Ninety-three adult patients (47 males and 46 females, median age 45 years) with aggressive localized non-Hodgkins lymphoma, 43 in stage I and 50 in stage II (non-bulky), were included in the study. Stage I patients received VACOP-B for 6 weeks plus involved field radiotherapy and stage II patients received 12 weeks VACOP-B plus involved field radiotherapy on residual masses. Eighty-six (92.5%) achieved complete remission and 4 (4.3%) partial remission. Three patients (3.2%) were primarily resistant. Ten-year probability of survival, progression-free survival and disease-free survival were 87.3, 79.9 and 83.9%, respectively. Eighty-four patients are surviving at a median observation time of 57 months (range: 6-126). Statistical analysis showed no difference between stages I and II in terms of response, ten-year probability of survival, progression-free survival or disease-free survival. Side effects and toxicity were negligible and were similar in the two patient groups. The results of this prospective study suggest that 6 weeks of VACOP-B treatment plus radiotherapy may be the therapy of choice in stage I aggressive non-Hodgkins lymphoma. Twelve weeks of VACOP-B treatment with or without radiotherapy was shown to be effective and feasible for stage II. These observations need to be confirmed by a phase III study comparing first and third generation protocols in stage I-II aggressive non-Hodgkins lymphoma.